In summary:

Fisher and Zahavi give different reasons for the costliness of the male character.

In Fisher's theory, the cost arose as the end-product of a runaway process. To begin with, long tails were not costly, but as an open-ended female preference for males with longer tails was selected into the population, the tails evolved past their optimum and ended up reducing the survival of their bearers.

In Zahavi's theory, the male character had to be costly from the start, and to remain costly as the female preference spread. The function of the chosen male character is to indicate genetic quality at other loci, and it has to be costly in order to be reliable.